4 Comparison with the old Arcetri spectral code

  Most of the lines considered in the old version of the Arcetri spectral code were calculated under the assumption that the population of the upper level of the transition j occurs mainly via excitation from the ground level g and the depopulation of level j occurs through spontaneous radiative decays. We may then express the power emitted per $\rm cm^{-3}$ by the transition $j\to k$ of the ion X^+m following Kato (1976) and Stern et al. (1978) as

$$P_{jk} = {{N{\left({X^{+m}}\right)}}\over{N{\left({X}\right)... ...{N_{\rm H}}}~{{N_{\rm H}}\over{N_{\rm e}}}~C_{gj}~E_{jk}~B_{jk}$$ (6)

where E_jk is the energy involved in the transition $j\to k$ and B_jk is the radiative branching ratio. The collisional excitation rate is given by (Kato 1976)

$$C_{{\rm g}j} = 8.63\ 10^{-6} \exp^{-{{E_{{\rm g}j}}}\over{kT}}~T^{-{1\over 2}}~{\Omega_{{\rm g}j}\over{\omega_{\rm g}}}$$ (7)

where $\omega_{\rm g}$ is the statistical weight of the ground level and $\Omega_{{\rm g}j}$ is the collision strength from the ground level. We are mainly interested in allowed transition and therefore the collision strength may be computed as

$$\Omega_{{\rm g}j} = {{8\pi}\over{\sqrt{3}}}~{\omega_g \over{E_{{\rm g}j}}}~f_{{\rm g}j}~\-g$$

with $E_{{\rm g}j}$ in Rydberg. $f_{{\rm g}j}$ is the oscillator strength of the transition and $\-{\rm g}$ is the Gaunt factor, computed according to Mewe et al. (1985). For the He & Li isoelectronic sequence use is made of the procedure given by Mewe (1972) and Mewe et al. (1981), and for details on transition from metastable levels we refer the reader directly to Landini & Monsignori Fossi (1990).

In the present update of the Arcetri spectral code we have renewed the database of oscillator strengths for the ions included in the old version. In the recent past several new calculations of radiative transition probabilities have been carried on in order to match the increasing need for very accurate radiative data. The Opacity Project (Seaton et al. 1992) results has been adopted for most of the transitions included in the new version of the Arcetri spectral code. Oscillator strengths obtained in the Opacity Project are reported in Verner et al. (1996). Since in the Opacity Project calculation relativistic effects are neglected, LS coupling is assumed. Verner et al. (1996) calculated oscillator strengths for each individual line of the LS multiplet assuming the LS coupling rules (Russel 1936). This procedure may introduce some uncertainties in the resulting fine-structure oscillator strengths, nevertheless the values thus obtained are still much more reliable than those included in the old version of the Arcetri code, since the latter were based on much older and less refined calculations. In a few cases very large differences are seen. Other sources for oscillator strengths are Fawcett (1986a) (O-like ions), 1986b (S-like ions) and (1986c) (P-like ions) and Shirai et al. (1987) (Nickel Ions).

New recent calculations of oscillator strengths have also permitted to add to the code a large number of new levels. The new dataset adopted in this version of the Arcetri spectral code allows the calculation of the theoretical emission of a far larger number of lines than the previous version.

In order to understand whether the changes in the atomic data affected the resulting theoretical line intensities we have performed a detailed comparison between the old and the new versions of the Code. A critical discussion is given in the following sections.

The old version of the Arcetri spectral code allowed the full calculation of the level population only for the Iron ions and the most abundant elements of the Beryllium, Carbon and Nitrogen isoelectronic sequences (hereafter group 1 lines); while the line emission of all the other ions was calculated using the approximation described at the beginning of this section (group 2).

4.1 Group 2 transitions

As expected, the comparison between group 2 transitions shows very often marked differences. We have compared lines belonging to the most abundant ions longward of 12 Å.

The differences between singlet lines may be higher than an order of magnitude, and normally it is found that the old version of the Code overestimates the new version's results. It is also interesting to note that the differences between most of the lines are temperature dependent, and sometimes this dependence is very strong (up to a factor of 2). Nevertheless the differences between strong lines such as the Magnesium-like 3s^{2 1}S - 3s3p ¹P are very small.

The old version of the Code most often reported transitions between LS coupled terms and therefore these multiplets were summed. The level population calculations of the new Code are carried on considering individual fine structure atomic levels and allows proper consideration of each line of the multiplet. This is a great improvement in most cases since the wavelength differences between each of the lines belonging to the multiplet are often of several Angstroms, much greater of the resolving power of all the modern spectrometers. The differences between the emissivities calculated by the two versions rise very often up to an order of magnitude and are temperature dependent in most cases. Again, the old emissivities are usually greater then the new ones. The differences between very strong lines such as the Lithium-like 2s ²S - 2p ²P and Sodium like 3s ²S - 3p ²P doublets are much smaller, tipically around 20$\%$.

4.2 Beryllium-like ions

Beryllium-like C III lines show larger differences (up to 40$\%$). This is due to the different adopted data, since the old code uses one electron distorted wave collision strengths (Bhatia & Kastner 1993c) while the present version includes R-Matrix results (Berrington et al. 1985, 1989). In the case of such a light ion the resonances may play a very important role in determining the total collision strength of transitions. O V differences are limited to 20$\%$ and are due to changes in the radiative transition probabilities. Similar differences are also found in Fe XXIII, due to the change of collisional transition probabilities for the three lowest configurations, since the old code adopts Bhatia & Mason (1986) three energies distorted wave collision strengths while the CHIANTI database uses the six energies relativistic distorted wave calculations of Zhang & Sampson (1992). More dramatic differences are found for Ne VII, Mg IX and Si XI, where differences rise up even to a factor of 10. The CHIANTI adopted atomic model for these ions includes also n=3 levels, and a metastable level $\rm 2p3d$ ³F₄ is found for which no radiative transition probability is available in literature. This causes this level to be strongly populated altering the population of all levels, leading to great differences from the old code atomic model which included only the n=2 levels. Work is in progress to exclude these levels from the statistical equilibrium but further work is recommended for radiative transition probabilities in the Beryllium isoelectronic sequence.

4.3 Carbon-like ions

  The differences arising between the Carbon-like ions are mainly due to the fact that for several of them the collisional data between the $\rm 2s^22p^2$, $\rm 2s2p^3$ and $\rm 2p^4$configurations have been changed. The old version of the Code used for these ions distorted wave collision strengths (Bhatia & Kastner 1993b; Bhatia & Doschek 1993a-c and 1995; Mason et al. 1979), while the CHIANTI database adopted R-Matrix effective collision strengths (Lennon & Burke 1994; Aggarwal 1983, 1984, 1985, 1986 and 1991). The differences between the two spectral codes are significant but not very large. The lighter ions (O III and Ne V) show differences up to 30$\%$, due to the fact that the R-Matrix approximation takes into account more properly the resonance contributions. The higher ions Ca XV and Fe XXI instead show a better agreement, with differences always smaller than 15$\%$. This is as expected since the distorted wave is a valid approximation for highly ionized systems. Differences between the S XI lines rise up to 20$\%$, due to the fact that the old code adopts the one-electron collision strengths of Bhatia et al. (1987b), while the CHIANTI database includes the Mason & Bhatia (1978) three-energies collision strengths, allowing therefore a more precise calculation of the effective collision strengths.

4.4 Nitrogen-like ions

The data for Nitrogen-like ions, Mg VII, Si IX, Ca XVII and Ni XXV have not been changed and therefore we expect identical results. Nevertheless very small differences (smaller than 5$\%$ in most cases, always smaller than 10$\%$) are found for several transitions. This is due to the fact the collision strengths and the effective collision strengths of the old code have been scaled according to scaling laws different from those adopted in the CHIANTI database and the new version of the code. Both scaling laws are derived from the work of Burgess and Tully (1992), but there are some differences in considering the high energy limit and the forbidden transitions scaling laws. The fact that there is a very good agreement between calculations performed with the same data but different ways of scaling them is a strong evidence that the use of the scaling laws themselves does not affect significantly the resulting calculated emissivities.

4.5 Iron ions

The old code included data for the Iron ions from Fe IX to Fe XXIII, and a brief description of the Iron database is given in Monsignori Fossi & Landini (1996). This selection of atomic data was very careful and covered all the existing Iron ions literature up to 1994. Nevertheless in the last four years a number of new calculations have been performed for many Iron ions and these have been included in the CHIANTI database and therefore in the new version of the Arcetri code. The data for Fe XVI, XVII, XIX and XX are identical and therefore the differences between the two codes are smaller than 5% and are due to the slight difference between the scaling of the electron collisional data such as for the N-like ions.

CHIANTI Fe IX radiative transition probabilities have been calculated using the program SUPERSTRUCTURE (Eissner et al. 1974) during the development of the CHIANTI database by P.R. Young, adopting 11 configurations ($\rm 3s^23p^6$, $\rm 3s^23p^53d$, $\rm 3s3p^63d$, $\rm 3s3p^53d^2$,$\rm 3s^23p^43d^2$, $\rm 3p^63d^2$, $\rm 3p^33d^3$, $\rm 3s^23p^54$l with l=0,1,2,3) and have been used in the present version of the Code. The most important difference between these values and those reported in the old version of the code (from Fawcett & Mason 1991) concerns the strong $\rm 3s^23p^6$ $\rm ^1$S - $\rm 3s^23p^53d$ $\rm ^1$P transition observed at 171.07 Å whose oscillator strength which shows a 25% difference between these two calculations. This difference is reflected in the calculated emissivity.

Fe X distorted wave and R-Matrix collision strengths have been calculated by Bhatia & Doschek (1995b) and Pelan & Berrington (1995) and adopted by CHIANTI. The differences between these calculations and the Mason (1975) ones adopted in the old code rise up to factor 2. This is a very important updating since some Fe X are very strong and widely observed in the EUV spectral range.

Bhatia & Doschek (1996) have calculated three energy distorted wave collision strengths for Fe XI whose inclusion in the CHIANTI database causes the new Arcetri code to be different from the old version which adopted the Mason (1975) results. The discrepancies rise up to a factor 2 for some transitions, but for most lines they are smaller than 40%. These differences are temperature dependent.

Fe XII atomic data and transition probabilities of the two Arcetri codes are the same but the new code includes more energy levels whose presence causes great differences between the results. In the new Arcetri code, some Fe XII lines have smaller emissivities than the old ones up to a factor 3.

The Fe XIII collisional transition probabilities are the same in the two versions of the code, but some differences are found in the radiative transition probabilities since the CHIANTI database adopted unpublished SUPERSTRUCTURE calculations obtained with a 24 configuration model. Most importantly, the CHIANTI Fe XIII atomic model includes also the $\rm 3s^23p3d$ ³F₄ metastable level whose population becomes significant at coronal densities and therefore influences the overall Fe XIII level population. This causes the two codes to be different up to 50%.

Storey et al. (1996) calculated R-Matrix effective collision strengths for the Fe XIV ground ²P_1/2 - ²P_3/2 transition but this is the only difference between the two versions of the code and, as already noted by Dere et al. (1997), this change of data does not alter significantly the results. We find discrepancies between the two datasets smaller than 10%.

Fe XV collisional transition probabilities have been calculated by Bhatia et al. (1996) (three-energies distorted wave collision strengths) and are adopted in CHIANTI. The old code adopted Christensen et al. (1985) results and great differences rise between the two codes. We have found that most transitions have differences up to 50%. It is worth noting that the very strong 284.16 Å transition shows agreement better than 10%.

Changes in Fe XVIII new code dataset have been made both in the radiative and collisional transitions probabilities. CHIANTI adopts A values from Blackford & Hibbert (1994), and relativistic distorted wave collision strengths from Sampson et al. (1991), while the old code takes all data from Cornille et al. (1992). Nevertheless it is found that the differences between the calculated emissivities are limited to less than 20%, consistently with the good agreement found in the two sets of collision strengths.

Fe XXI collisional data have been changed and Aggarwal (1991) data have been adopted in the new code, nevertheless, as noted in Sect. 4.3, agreement better than 15% is found between the two codes.

Fe XXII data have been improved with Zhang et al. (1994) and Zhang & Sampson (1995) calculations, increasing the number of included energy levels (20 in the old code, 125 in the new one). This results in big differences in the output of the two codes.

For Fe XXIII, Zhang & Sampson (1992) relativistic distorted wave collision strengths have been adopted by CHIANTI and the new Arcetri code, replacing the older Bhatia & Mason (1986) calculations. Nevertheless differences for Fe XXIII emission lines (including the very  strong 132.8 Å line) are limited to less than 30%.

No data were available in the old Arcetri code for Fe II, VII, VIII, XXIV.

Though many important lines do not show appreciable changes, the new Arcetri database represents a great advance for plasma diagnostics and synthetic spectra with the Iron ions, since it adopts more recent data which allow a more precise calculation of level population and line emission.